Let F:ℱ ℳ → ℬ be a vector bundle functor. First we classify all natural operators transforming projectable vector fields on Y to functions on the dual bundle (FY)* for any -object Y. Next, under some assumption on F we study natural operators lifting horizontal 1-forms on Y to 1-forms on (FY)* for any Y as above. As an application we classify natural operators for some vector bundle functors F on fibered manifolds.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-1, author = {J. Kurek and W. M. Mikulski}, title = {The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds}, journal = {Colloquium Mathematicae}, volume = {96}, year = {2003}, pages = {141-149}, zbl = {1052.58004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-1} }
J. Kurek; W. M. Mikulski. The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds. Colloquium Mathematicae, Tome 96 (2003) pp. 141-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-1/